U.S. patent number 5,010,473 [Application Number 07/401,996] was granted by the patent office on 1991-04-23 for method and apparatus for model-based control of an open-loop process.
This patent grant is currently assigned to Duke University. Invention is credited to James R. Jacobs.
United States Patent |
5,010,473 |
Jacobs |
April 23, 1991 |
Method and apparatus for model-based control of an open-loop
process
Abstract
A method and apparatus for controlling a model based open-loop
process and more specifically, the concentration of a drug
delivered intravenously to a patient as a function of the rate of
infusion. A three-compartment pharmacokinetic model is preferably
used to determine the plasma drug concentrations corresponding to
two arbitrarily selected rates of infusion. Based upon the linear
relationship between corresponding data pairs, each pair comprising
a rate of infusion and a corresponding plasma drug concentration,
an interpolated rate is determined by a microprocessor (100) as a
function of a specified plasma drug concentration, in accordance
with program steps stored in a read only memory (ROM) 104. The
actual infusion rate of the drug during successive time intervals
is repetitively used to compute the plasma drug concentration at
the end of each time interval. In each successive iteration, state
variables from the previous computation of the plasma drug
concentration are used to determine the next interpolated infusion
rate. Any interruptions in the output from an infusion device (112)
and variations from the interpolated value of the infusion rate are
compensated. Using this open-loop control method and apparatus, the
specified plasma drug concentration is rapidly achieved.
Inventors: |
Jacobs; James R. (Durham,
NC) |
Assignee: |
Duke University (Durham,
NC)
|
Family
ID: |
23590111 |
Appl.
No.: |
07/401,996 |
Filed: |
August 31, 1989 |
Current U.S.
Class: |
700/30;
604/65 |
Current CPC
Class: |
A61M
5/172 (20130101); G05B 13/04 (20130101); A61M
2005/14296 (20130101) |
Current International
Class: |
A61M
5/172 (20060101); A61M 5/168 (20060101); G05B
13/04 (20060101); G05B 013/04 (); A61M
005/172 () |
Field of
Search: |
;364/148,149,150,153
;604/151,891,51,66,31,890.1,65 ;128/734 |
References Cited
[Referenced By]
U.S. Patent Documents
|
|
|
4280494 |
July 1981 |
Cosgrove, Jr. et al. |
4533346 |
August 1985 |
Cosgrove, Jr. et al. |
4741732 |
May 1988 |
Crankshaw et al. |
4810243 |
March 1989 |
Howson |
4880014 |
November 1989 |
Zarowitz et al. |
|
Primary Examiner: Smith; Jerry
Assistant Examiner: Gordon; Paul
Attorney, Agent or Firm: Christensen, O'Connor, Johnson
& Kindness
Claims
What is claimed is:
1. A method for controlling a process to obtain a specified output,
O.sub.s, where the process is described by a linear model that
defines an output of the process as a function of a specified
control signal, wherein the control signal controls an actuator
that affects the process, said method comprising the steps of:
(a) arbitrarily selecting a first value, X.sub.1, and a second
value, X.sub.2, for the control signal, and initializing a
plurality of state variables in the model;
(b) as a function of the first and second values of the control
signal, which are respectively input to the model, determining
corresponding first and second output values, O.sub.1 and O.sub.2,
that would be obtained at the end of an interval of time, .DELTA.t,
were the control signal to be applied for this interval;
(c) interpolating with respect to the first and second values of
the control signal and corresponding first and second output values
to determine a desired value, X.sub.d, for the control signal that
should produce the specified output, O.sub.s, at the end of the
time interval, .DELTA.t;
(d) for the time interval, .DELTA.t, operating the process using
the desired value, X.sub.d, determined in step (c) for the control
signal;
(e) determining a value, X.sub.a, of the control signal actually
used by the actuator during the time interval, .DELTA.t;
(f) using the model, determining a computed value for the output,
O.sub.c, as a function of the value of the control signal
determined in step (e); and
(g) reiteratively repeating steps (b) through (f), each successive
iteration using values for the state variables in the model that
depend on the computed value of the output determined in step (f)
of the previous iteration, so that control of the process tracks
changes in the specified output and the process quickly converges
on the specified output.
2. The method of claim 1, wherein the step of interpolating
comprises the steps of:
(a) determining the difference between the second and first control
signals, X.sub.2 -X.sub.1 ;
(b) determining the difference between the second and first
corresponding output values, O.sub.2 -O.sub.1 ;
(c) determining a slope of a line through a data pair (O.sub.1,
X.sub.1) and a data pair (O.sub.2, X.sub.2), from the
relationship:
(d) determining the desired control signal, X.sub.d, as a function
of the specified output, O.sub.s, from the relationship:
3. The method of claim 1, wherein the process includes constraints
on the values of the control signal that can be used by the
actuator, and wherein the step of operating the process for the
predetermined time interval includes the step of using a value for
the control signal that approximates the desired value of the
control signal as closely as the constraints allow.
4. The method of claim 3, wherein the constraints comprise limits
on the maximum and minimum values of the control signal.
5. The method of claim 3, wherein the constraints comprise limits
on the usable resolution for the values of the signal
parameters.
6. The method of claim 3, wherein the actual control signal used
may be substantially unequal to the desired control signal X.sub.d
for one or more time intervals due to an actuator fault, said step
of determining the control signal actually used by the actuator
including the step of computing a change in the output during a
total accumulated time that the actuator fault continues, so that
upon correction of the actuator fault, the step of determining the
desired value of the control signal compensates for the total time
in which the actuator was not responding to the desired control
signal.
7. The method of claim 1, wherein the model is linear with respect
to successive data pairs, each data pair comprising a control
signal and a corresponding process output.
8. The method of claim 1, wherein the time interval is of a
predetermined length unless an event is detected that alters the
operation of the process or the specified output, causing the time
interval to terminate prematurely.
9. A method for controlling the concentration of a drug
administered intravenously at a controlled rate to a recipient to
achieve a specified plasma drug concentration, wherein a linear
pharmacokinetic model is used that predicts the plasma drug
concentration as a function of the rate administered and as a
function of a plurality of state variables and other parameters
that define the current concentration of the drug in the
recipient's body, said method comprising the steps of:
(a) arbitrarily selecting a first and a second rate for
administering the drug during an interval of time;
(b) using the model, determining a first and a second plasma drug
concentration corresponding respectively to the first and second
rates, if said rates were used during the interval of time;
(c) from the first and second rates and the first and second plasma
drug concentrations, determining an interpolated drug delivery rate
that should produce the specified plasma drug concentration of the
drug in the recipient at the end of the interval of time;
(d) delivering the drug to the recipient nominally at the
interpolated rate for the interval of time;
(e) determining an actual rate at which the drug is being delivered
to the recipient;
(f) using the model, determining a computed plasma drug
concentration that corresponds to the actual rate and setting the
plurality of state variables as a function of the computed plasma
drug concentration; and
(g) reiteratively repeating steps (b) through (f) for successive
intervals of time, each iteration determining the interpolated rate
using the model, wherein the plurality of state variables for that
iteration depend on the computed plasma drug concentration from the
previous iteration, thus compensating for any substantial variation
between the interpolated rate of delivery and the actual rate,
whereby the rate of delivery of the drug is controlled so that the
specified plasma drug concentration is rapidly achieved.
10. The method of claim 9, wherein the drug is delivered to the
recipient by an infusion device, said infustion device being
operable to deliver the drug only at specific incremental rates,
said step of delivering the drug at the interpolated rate
comprising the step of delivering the drug at one of the specific
incremental rates that is closest to the interpolated rate.
11. The method of claim 10, wherein the step of determining the
actual rate includes the step of determining said one specific
incremental rate used to deliver the drug.
12. The method of claim 10, wherein the step of determining the
actual rate includes the step of determining if the drug was not
delivered to the recipient by detecting a fault in the infusion
device.
13. The method of claim 10, wherein the step of determining the
actual rate includes the step of determining if the drug was not
delivered to the recipient by detecting an occlusion in a line
through which the drug is delivered to the recipient from the
infusion device.
14. The method of claim 13, wherein the step of determining the
interpolated rate compensates for non-delivery of the drug to the
recipient for successive intervals of time, when delivery of the
drug is again resumed, because the plurality of state variables
changes as the computed plasma drug concentration changes during
the time that the drug is not delivered to the recipient.
15. The method of claim 9, wherein the interval of time is of a
predetermined duration, subject to a premature termination in
response to the occurrence of a specified event affecting the
actual drug delivery rate.
16. Apparatus for controlling a process to obtain a specified
output, O.sub.s, where the process is described by a model that
defines an output of the process as a function of a specified
control signal and wherein the process is affected by an actuator
in response to the control signal, said apparatus comprising:
(a) processor means for:
(i) arbitrarily selecting a first value, X.sub.1, and a second
value, X.sub.2, for the control signal that could be applied to
control the actuator for a time interval, .DELTA.t;
(ii) initializing a plurality of state variables used in the
model;
(iii) as a function of the first and second values of the control
signal, which are input to the model, respectively determining
first and second output values, O.sub.1 and O.sub.2 ; and
(iv) interpolating with respect to the first and second values of
the control signal and corresponding first and second output values
to determine a desired value, X.sub.d, for the control signal that
should produce the specified output at the end of the time
interval;
(b) means for determining successive time intervals and producing
time signals indicative of each of said time intervals;
(c) said processor means being connected to receive said time
signals and being further operative to operate the process using a
closest available control signal to the desired value X.sub.d ;
and
(d) means for determining an actual value of the control signal
implemented during operation of the actuator during the interval of
time; said processor means being further operative to determine a
computed value, O.sub.c, for the output of the process as a
function of the actual value, X.sub.a, of the control signal, and
to repetitively and reiteratively determine the desired value,
X.sub.d, for successive intervals of time, using values for the
plurality of state variables in the model that depend on the
computed value of the output determined in a preceding iteration,
so that the process rapidly converges on the specified output.
17. The apparatus of claim 16, wherein the processor means comprise
a microprocessor and a nonvolatile electronic memory in which is
stored a program directing the operation of the microprocessor.
18. The apparatus of claim 16, wherein the means for determining an
actual value of the control signal comprise means for determining
that the actuator was interrupted during one or more of the time
intervals, preventing the specified value of the output from being
realized.
19. The apparatus of claim 16, wherein the process or means
interpolate by:
(a) determining the difference between the second and first control
signals, X.sub.2 -X.sub.1 ;
(b) determining the difference between the second and first
corresponding output values, O.sub.2 -O.sub.1 ;
(c) determining the slope of a line through a data pair (O.sub.1,
X.sub.1) and a data pair (O.sub.2, X.sub.2), from the
relationship:
(d) determining the desired control signal, X.sub.d, as a function
of the specified output, O.sub.s, from the relationship:
20. Apparatus for controlling the intravenous administration of a
drug to a recipient at a controlled rate to achieve a specified
plasma drug concentration, wherein a linear model is used that
determines the plasma drug concentration as a function of the rate
at which it is administered and as a function of a plurality of
state variables and other parameters that define the current
concentration of the drug in the recipient's body, said apparatus
comprising:
(a) processor means, for:
(i) selecting a first and a second arbitrary rate for administering
the drug during a time interval .DELTA.t;
(ii) using the model, determining a first and a second plasma drug
concentration that corresponds to the first and second arbitrary
rates for administering the drug; and
(iii) based on the first and second arbitrary rates and
corresponding first and second plasma drug concentrations,
determining an interpolated drug delivery rate that should produce
the specified plasma drug concentration of the drug in the
recipient at the end of the time interval;
(b) infusion means, connected to the processor means, for
delivering the drug to the recipient nominally at the interpolated
rate;
(c) timer means for determining successive intervals of time, said
timer means producing time signals that indicate the duration of
each time interval; and
(d) means for determining an actual rate at which the drug is
administered to the recipient by the infusion means; said processor
means being further operative to apply the model to determine a
computed plasma drug concentration that corresponds to the actual
rate during a current time interval, where the plurality of state
variables used in the model vary as a function of the computed
plasma drug concentration from prior time intervals, and being
still further operative to determine an interpolated drug delivery
rate and a computed plasma drug concentration using the model, for
successive intervals of time, and thereby controlling the infusion
means to operate substantially at the interpolated drug delivery
rate so that the computed blood plasma concentration rapidly
approaches the specified plasma drug concentration.
21. The apparatus of claim 20, wherein the means for determining
the actual rate at which the drug is administered comprise an
occlusion detector to detect if an occlusion of a delivery line
connecting the infusion means to the recipient has prevented the
drug from being delivered to the recipient.
22. The apparatus of claim 20, wherein the means for determining
the actual rate at which the drug is administered comprise a fault
detector that can detect a failure in the infusion means, which
prevents the drug from being delivered to the recipient.
Description
TECHNICAL FIELD
This invention generally pertains to a model-driven method and
apparatus for controlling an open-loop process, and specifically,
to controlling the rate at which a drug is administered to a
recipient to achieve a specified plasma drug concentration.
BACKGROUND OF THE INVENTION
Most process control schemes are closed-loop, depending upon a
feedback signal that either directly or indirectly indicates the
effect on the process output of changes in the output of one or
more actuators. In an open-loop control process, a feedback signal
is normally not available, typically because the output of the
process is difficult, expensive, or impossible to monitor in a
timely fashion. Open-loop processes are sometimes automatically
controlled by using a model to predict the process output as a
function of the output from the controlled actuator. The accuracy
with which the process is controlled then depends simply on how
accurately the model reflects the actual behavior of the
process.
For example, a physician using an infusion device (actuator) to
administer a drug intravenously to a patient may program an
infusion device controller to achieve user-specified plasma drug
concentrations based on a pharmacokinetic model of the drug being
infused. The infusion device controller uses the pharmacokinetic
model to dynamically determine the drug delivery rate at which the
infusion device should be operated to achieve the specified plasma
drug concentration. The infusion device infuses drug to the
recipient, and the drug becomes present within the plasma of the
recipient at some concentration. Ideally, the ability of the
infusion device controller and the infusion device to achieve the
specified plasma drug concentration would depend on the accuracy
and applicability of the pharmacokinetic model. However, most drug
infusion devices have a limited range of delivery rates, and a
limited resolution for specifying or controlling the delivery rate.
If the control method computes a delivery rate that is outside the
available range of delivery rates and/or the actual delivery rate
does not equal the computed rate due to lack of resolution of the
infusion device, a significant difference between the theoretical
and actual plasma drug concentrations may develop over time.
Furthermore, if, for example, sensors within the infusion device
detect an occlusion of the catheter line connecting the infusion
device to the recipient and cause the infusion device to halt drug
delivery, the theoretical and actual plasma drug concentrations may
diverge unless the controller and pharmacokinetic simulation are
advised of the interruption in drug delivery and compensate
accordingly once drug delivery is resumed. Thus, in a model-based
control method, the model simulation must be apprised of the actual
output of the actuator (input to the process), not the desired
output of the actuator.
SUMMARY OF THE INVENTION
In accordance with the present invention, a method and apparatus
are provided for controlling a process to obtain a specified
output, O.sub.s, where the process is described by a model that
defines an output of the process as a function of a specified
control signal. The first step in the method provides for
arbitrarily selecting a first value, X.sub.1, and a second value,
X.sub.2, for the control signal, and initializing a plurality of
state variables in the model. First and second output values,
O.sub.1 and O.sub.2, that would be obtained at the end of a time
interval, .DELTA.t, were the control signal to be applied for this
time, are then determined as a function of the first and second
values of the control parameter using the model. Assuming that a
linear relationship exists between data pairs (O.sub.1, X.sub.1)
and (O.sub.2, X.sub.2), the method interpolates with respect to
these data pairs, to determine a desired value, X.sub.d, for the
control signal that should produce the specified output.
During the time interval, the process is operated nominally using
the desired value, X.sub.d, for the control signal. While the
process is being operated, a value, X.sub.a, of the control signal
actually used in the process is determined. Using the model, a
computed value for the process output, O.sub.c, is determined as a
function of the value, X.sub.a, of the control signal. Each of
these steps is reiteratively repeated, each successive iteration
using values for state variables in the model that depend on the
computed value of the process output determined in a previous
iteration. As a result, the actual process output is tracked,
causing the process to quickly converge on the specified
output.
The step of interpolating includes the steps of determining the
difference between the second and first control signals, X.sub.2
-X.sub.1, and the difference between the second and first
corresponding output values, O.sub.2 -O.sub.1. Thereafter, the
slope of a line through the data pair (O.sub.1, X.sub.1) and the
data pair (O.sub.2, X.sub.2) is determined from the
relationship:
The desired control parameter, X.sub.d, is then determined from the
relationship:
In a case where the process includes constraints on the values of
the control signal that can be used in the process, the step of
operating the process for the time interval includes the step of
using a value for the control signal that approximates the desired
value of the control signal as closely as the constraints allow. As
an example, the constraints may comprise limits on the maximum
and/or minimum values of the control signal. Alternatively, the
constraints may comprise limits on the resolution of the values of
the control signal usable in the process.
If the actual control signal substantially equals zero for one or
more of the time intervals due to a process fault, the step of
determining the control signal, X.sub.a, actually implemented in
the process includes the step of computing a change in the output
during a total accumulated time that the process fault continues.
As a result, upon correction of the process fault, the step of
determining the desired value of the control parameter compensates
for the total accumulated time in which the process was not
operated with the desired control signal.
More specifically, the method may relate to controlling the
concentration of a drug administered intravenously at a controlled
rate to a recipient to achieve a specified plasma drug
concentration, wherein a linear pharmacokinetic model is used that
predicts the plasma drug concentration as a function of the rate
the drug is administered and as a function of a plurality of state
variables and other parameters that define the current
concentration of the drug in the recipient's body. Analogous steps
in practicing this method are included as a further aspect of the
invention. Apparatus including a plurality of means for carrying
out the functions defined as steps in the above method comprise a
further aspect of the invention.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram illustrating the steps implemented in
model-based control of an open-loop process to achieve a specified
output;
FIG. 2 is a block diagram showing the steps of the method in the
present invention as applied to obtaining a specific plasma
concentration of a drug administered by intravenous infusion,
wherein the actuator is an infusion device having a controlled
delivery rate for infusing the drug into a recipient;
FIG. 3 is a block diagram of a microprocessor control for a drug
infusion device;
FIG. 4 is a graph illustrating the plasma concentration of a drug
at a time, t, in respect to the plasma drug concentrations
corresponding to two arbitrary delivery rates, at a time,
t+.DELTA.t;
FIG. 5 is a graph illustrating an interpolation step used to
compute a desired rate of infusion to achieve the specified plasma
drug concentration;
FIG. 6 is a schematic representation of a three-compartment
pharmacokinetic model of drug assimilation in the body for use in
determining the plasma concentration of the infused drug;
FIG. 7 is a transfer function defining the three-compartment model
of drug disposition in the body; and
FIGS. 8-10 represent equations defining the concentration of the
drug in each of the three compartments of the model of FIG. 6.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
Although the present invention was developed specifically for
controlling the rate of intravenous infusion of a drug to achieve a
specified plasma drug concentration, it must be emphasized that the
invention has general application to any model-based control
paradigm where the relationship between time, the output of the
controlled actuator (input to the process), and the output of the
process are described by a linear dynamic model. Details of the
particular model used to calculate the output of the process as a
function of the actuator output are not important to the present
invention. However, the accuracy with which the specified process
output is obtained does depend upon the quality of the model used.
To emphasize this point, FIG. 1 includes a block diagram that
schematically defines how such an open-loop process is controlled
to achieve the specified output using a model-based control
paradigm. It is presumed that the value of the actual output of the
process is either difficult or impossible to measure in a timely
fashion, or is otherwise not available as feedback signal for use
in a conventional, real-time, closed-loop control of the
process.
As shown in FIG. 1, a value for the specified output of the process
is input to a block 10. In block 10, a first and a second value for
the actuator output, which nominally determine the output of the
process, are arbitrarily selected. These first and second values
must not be equal to each other and should preferably be within a
range relevant to the control process, but are otherwise entirely
arbitrary. A block 12 includes parameters and constants of
equations that model and simulate the process to be controlled as a
function of an actuator output and as a function of time intervals,
.DELTA.t. With the model state variables initialized to their state
at the end of the most recent time interval, .DELTA.t.sub.n-1, a
first arbitrarily selected value for the actuator output (input to
process) to be used during .DELTA.t.sub.n is used as an input to
the model to calculate the output value that would be obtained at
the end of .DELTA.t.sub.n. With the model similarly initialized, a
second arbitrary selected value for the actuator output (input to
process) to be used during .DELTA.t.sub.n is used as an input to
the model to calculate the output value that would be obtained at
the end of .DELTA.t.sub.n.
Since the model responds linearly to changes in input, a linear
relationship exists with respect to data pairs that each include
one of the arbitrarily selected first and second values for the
actuator output and the computed value for the output of the
process corresponding to that value for the period .DELTA.t.sub.n.
Because of this linear relationship, it is possible to interpolate
along a line extending through these two data pairs to determine an
interpolated actuator control signal that should nominally be used
during the next time interval to achieve or maintain the specified
process output.
The interpolated signal is provided to a block 14 for controlling
an actuator to modify the output of the process. This relationship
is indicated by the arrow connecting block 14 to a block 16. Block
16 is labeled Process, and generally represents the plant or other
mechanism in which the process is effected. The "actual output"
developed by the process in block 16 represents a quantity that
would normally be used as a feedback signal for closed-loop control
of the process, if this output could readily be measured in a
timely fashion.
If the actuator is able to respond precisely to the interpolated
control signal, the actual output from block 16 should equal the
desired process output by the end of the first sampling interval,
at least within the accuracy limits of the model. However, if the
interpolated control signal is outside of the actuator's range, or
if the actuator cannot respond with as much resolution as the
control signal specifies, or if the actuator is nonfunctional for
some portion of the time interval, then the actual process output
will differ from that specified.
The present invention compensates for the failure of the actuator
to use the interpolated control signal determined in block 10
exactly by using a signal indicative of the actual output of the
actuator. This signal is input to a block 18. In block 18, the
model parameters and equations from block 12 are used to determine
a computed process output that corresponds to the actual actuator
output used in controlling the process in block 16 and the actual
duration of the sampling interval. The computed output of the
process may differ from the specified output due to a failure in
the actuator, lack of resolution or precision in the ability of the
actuator to use the interpolated control signal, or because the
interpolated control signal lies outside the available range of the
actuator. Since the state variables in the model used to derive the
interpolated control signal are computed from the actual
performance of the actuator, not the desired performance of the
actuator, the interpolated control signal is inherently and always
that which is optimally suited to achieve the desired process
output during the next sampling interval.
At the end of each sampling interval, determined by a timer in a
block 20, a switch 22 is closed and the computed output from block
18 is input to block 10. At the same time, a plurality of state
variables developed in the equations that define the model as a
function of the actual actuator output used as the input to the
simulation of the process in block 18 are input to block 10 through
a switch 24. This switch is also controlled by the timer in block
20. The timer in block 20 may operate at regular predefined
intervals or may also be interrupt- or event-driven.
In block 10, at the end of each preceding sampling interval, the
arbitrarily selected first and second values for the actuator
output are respectively input to the model to calculate
corresponding first and second simulated process output values, and
a new interpolated control signal is determined based on the liner
relationship between the resulting data pairs and the specified
process output value. Each successive time that a new interpolated
control signal is thus determined (for a period .DELTA.t.sub.n),
the model is first updated with the state variables from the
previous iteration (for the preceding period .DELTA.t.sub.n-1),
which are provided from block 18 and which depend upon the actual
actuator output used during the previous interval of time
(.DELTA.t.sub.n-1). Using this method, the actual output of the
process approaches the specified output and tracks interruptions or
variations in the operation of the actuator.
Turning now to FIG. 2, the specific application of the present
invention to obtaining a specified plasma concentration of a drug
administered intravenously is illustrated in a schematic block
diagram, similar to that of FIG. 1. The desired plasma drug
concentration is input to a block 40. Note that in this disclosure,
the word "plasma" may be used interchangeably with words suggesting
other constituents of blood (e.g., whole blood, serum, free
fraction), depending on the particular implementation and
application. Arbitrary infusion rates are selected and used as
separate inputs to a linear pharmacokinetic model for the drug for
calculation of two corresponding plasma drug concentrations that
would be obtained if the selected infusion rates were to be
utilized during the next time interval. Based upon the linear
relationship between corresponding data pairs comprising the first
and second arbitrarily selected infusion rates and the
corresponding plasma drug concentrations, a desired infusion rate
for the drug is determined by interpolation with respect to the
desired plasma drug concentration. Details of the interpolation
process are graphically illustrated in FIGS. 4 and 5.
With the pharmacokinetic model initialized to its state at the end
of the previous infusion interval, .DELTA.t.sub.n-1, a first
arbitrarily selected infusion rate X.sub.1 is input to the model
defined by parameters provided from a block 42. Using the model, a
first plasma drug concentration, O.sub.1, that would result at the
end of the impending infusion interval, .DELTA.t.sub.n, if the drug
at the first arbitrarily selected infusion rate X.sub.1 were to be
delivered by the infusion device for the internal .DELTA.t.sub.n is
determined. Similarly, a second plasma drug concentration, O.sub.2,
that would result at the end of the impending infusion interval,
.DELTA.t.sub.n, if the drug at a second arbitrarily selected
infusion rate X.sub.2 (different than X.sub.1) were to be delivered
by the infusion device for the interval .DELTA.t.sub.n, is
determined. A line 70 in FIG. 5 is drawn through the data pairs
(X.sub.1, O.sub.1) and (X.sub.2, O.sub.2). A specified plasma drug
concentration, O.sub.s, defines a point at a reference numeral 72
on line 70. A vertical line dropped from point 72 intercepts a
corresponding infusion rate at X.sub.d. Thus, the interpolated
infusion rate, X.sub.d, is the desired ideal infusion rate that
should be used during the infusion interval .DELTA.t.sub.n as an
input to a block 44 to control the infusion device for infusing
drug into the recipient. All of these calculations are made during
a time much, much smaller than .DELTA.t.sub.n so that they can be
considered to have been performed substantially instantaneously
during the time between the end of .DELTA.t.sub.n-1 and the start
of .DELTA.t.sub.n, even though .DELTA.t.sub.n-1 and .DELTA.t.sub.n
are step-wise continuous in time. The infusion of the drug into the
recipient's body is represented by the line connecting block 44 to
a block 46. Block 46 is labeled Recipient's Body, but in a larger
sense indicates the pharmacological process that determine the
actual plasma drug concentration. A recipient's body weight, sex,
age, and many other factors may affect the actual plasma drug
concentration resulting from a particular drug dosage, and some of
these factors may be embodied in the model parameters provided in a
block 42. The only variable controlled to achieve the specified
plasma drug concentration is the rate at which the drug is infused
into the recipient by the infusion device in block 44.
Although determined graphically in FIG. 5, the interpolated
delivery rate input to the infusion device in block 44 may also be
interpolated mathematically from the corresponding data pairs
(X.sub.1, O.sub.1) and (X.sub.2, O.sub.2) and specified plasma
concentration of the drug based on the relationship:
where b=(O.sub.2 -O.sub.1)/(X.sub.2 -X.sub.1)=slope of the line
through (X.sub.1, O.sub.1) and (X.sub.2, O.sub.2).
For the purposes of this disclosure and the claims that follow, the
term "interpolation" is intended to encompass both graphical and
numeric methods of determining the interpolated control signal or
ideal drug infusion rate.
The interpolation control signal or ideal drug infusion rate may
not be achieved if the infusion device in block 44 can only be set
to deliver the drug, for example, at integer values of an infusion
rate. Furthermore, the interpolated or desired ideal infusion rate
may exceed the maximum infusion rate at which the infusion device
in block 44 can deliver the drug into the recipient's body, and of
course the infusion device cannot remove drug from the recipient
(negative infusion rate). Also, an occlusion of the catheter line
connecting the infusion device to the recipient's body, or a fault
in the infusion device such as mechanical breakdown, may interrupt
drug delivery to the recipient. For these and other reasons, the
infusion device may infuse the drug at an actual infusion rate that
differs from the desired rate. The present invention compensates
for these limitations. A signal indicative of the actual infusion
rate is provided from block 44 to a block 48. In block 48, the
actual infusion rate is input to the model to compute a plasma
concentration of the drug that corresponds to the actual rate of
infusion of drug into the recipient. This " actual" infusion rate
is typically not a measured infusion rate but rather is the
infusion rate nominally reported by the infusion device, which
results from the electronic and/or mechanical properties of the
infusion device in the given circumstances.
Block 42 contains the model parameters, constants, and equations
that are used to define the simulation of the process in block 48
so that the theroretical plasma concentration can be computed. At
the end of an infusion interval .DELTA.t.sub.n, the timer in a
block 50 closes a switch 56 so that a signal indicative of the
actual infusion rate generated by the infusion device during
.DELTA.t.sub.n is input to block 48. At the end of an infusion
interval .DELTA.t.sub.n, determined by a timer in block 50, a
switch 52 is closed to provide the computed plasma concentration as
an input to block 40. In addition, the timer in block 50 closes a
switch 54 so that state variables corresponding to parameters in
the model that change with each computation of a new computed
plasma concentration are input to block 40. Also, after each
predetermined time interval, block 40 again determines the desired
infusion rate by interpolation between the data pairs comprising
the arbitrarily selected first and second delivery rates and
corresponding plasma concentrations that are determined each time
from the model. As this iterative process proceeds, the actual
plasma concentration in the recipient's body quickly approaches the
specified plasma concentration input to block 40 (unless infusion
of the drug is interrupted by an infusion device fault or an
occlusion of a catheter line, for example).
Switches 52, 54, and 56 conveniently represent gated data transfer
events and are not actual electrical switches. Typically, these
switches will be gated at the end of each particular sampling
interval .DELTA.t.sub.n, but the timer in block 50 that gates these
switches may be event- or interrupt-driven such that data transfer
occurs at a time before the scheduled end of .DELTA.t.sub.n.
Examples of events that would ideally result in the premature
termination of the current infusion period are when the
microprocessor detects an error or fault condition altering the
rate of drug delivery or when a new specified plasma drug
concentration is entered by the user into block 40. In any case,
the timer in block 50 determines the actual duration of each
sampling interval and reports that interval to the simulation in
block 48.
If a physician changes the value of the specified plasma
concentration of the drug that is input to block 40, the ideal or
desired infusion rate changes correspondingly. The state variables
that are transferred through switch 54 from block 48 to block 40
and the computed value for plasma concentration that are used in
each successive iteration compensate for the change in delivery
rate to achieve the new specified plasma concentrations. As shown
in FIG. 5, the value for the computed plasma concentration,
O.sub.c, at time t, forms a basis for computing the plasma
concentration corresponding to the arbitrarily selected rates of
infusion X.sub.1 and X.sub.2, at time t+.DELTA.t. In the preferred
embodiment, the timer in block 20 normally closes switches 52, 54,
and 56 at nine-second intervals, i.e., .DELTA.t=9 seconds, unless
interrupted prior to the end of that time. Due to the relatively
short time interval between iterations, the control method readily
tracks changes in the desired plasma concentration input by medical
personnel.
Referring to FIG. 3, a control that implements the above-described
method comprising one aspect of the present invention is
illustrated in a block diagram. The control includes a
microprocessor 100, which is connected to a random access memory
(RAM) 102 in which data is temporarily stored, and to a read-only
memory (ROM) 104 in which are defined program steps implemented by
the microprocessor for controlling the infusion device to deliver a
drug to a patient. A time base 106 is connected to microprocessor
100, and may comprise a crystal controlled oscillator or
conventional RC circuit, as is well known to those of ordinary
skill in the art. Using time base 106 as a time/frequency
reference, microprocessor 100 determines the predetermined interval
of time for each successive iteration in blocks 40 and 48. Also
connected to microprocessor 100 are a display 108 and a keypad 110.
In response to prompt messages made to appear on display 108,
medical personnel enter data describing characteristics of the
patient that are required by the model, the type of drug to be
infused, and the desired plasma concentration of the drug. The
prompt messages shown on display 108 comprise part of the program
steps stored in ROM 104, and the data entered by the medical
personnel are temporarily stored in RAM 102.
Microprocessor 100 controls an infusion device 112 to infuse the
drug as described above. Although control of infusion device 112
involves many other considerations, for purposes of this
disclosure, the primary control parameter effected in infusion
device 112 by the microprocessor is the rate at which the infusion
device delivers drug to the patient. Since the control including
microprocessor 100 is integral with infusion device 112 in the
preferred embodiment, the rate of infusion and resolution with
which this parameter is achievable by the infusion device are
stored in ROM 104 and are thus readily accessible by microprocessor
100. For example, infusion device 112 may have an operating range
of infusion rates of between 10 and 999 ml per hour, specifiable
only in integer values. Microprocessor 100 determines the actual
infusion rate (at least in part) from such data.
A drug reservoir 116 is connected to supply the drug at the
specific concentration to infusion device 112 through a supply line
118. The drug is typically infused intravenously into a recipient
122 through a catheter line 120. Infusion device 112 includes a
plurality of sensors for detecting fault conditions that can
prevent the infusion device from delivering the drug to a patient.
For example, the sensors can detect an occlusion in catheter line
120, and other fault conditions. In response to any such fault
condition, sensors 114 produce a binary signal indicating that the
drug is not being delivered to recipient 122. As noted above, the
actual infusion rate is determined by microprocessor 100, with
respect to the operating specifications for infusion device 112
that are stored within ROM 104, and also with respect to one or
more binary signals supplied to the microprocessor from sensors
114. Microprocessor 100 thus compensates for changes in the plasma
drug concentration caused by any interruption of drug infusion, by
using an actual infusion rate equal to zero during the simulation
of the process in block 48 of FIG. 2 while the interruption
continues. Once the fault is corrected and delivery of the drug to
the recipient is resumed, a non-zero value for the actual delivery
rate, which reflects the actual operating capabilities of the
infusion device is again input to block 48 to determine the current
value of computed plasma concentration of the drug, compensated for
the period of time in which drug was not infused into the
recipient.
To better appreciate the advantages of the present invention in
controlling the open-loop drug infusion process represented in FIG.
2, it is helpful to understand a specific model used for
calculating the plasma concentration of a drug as a function of the
rate at which the drug is infused into a recipient's body. For this
purpose, a three-compartment, open pharmacokinetic model is
illustrated in FIG. 6. In this model, the rate of drug infusion is
represented by the variable k.sub.0 (t) and the rate constant for
drug elimination from the body by the constant k.sub.10. The plasma
drug concentration is identified by the variable C.sub.1 (t). The
apparent volume of the central or plasma compartment is V.sub.1.
The two other compartments in the model include drug concentrations
identified respectively by the terms C.sub.2 (t) and C.sub.3 (t)
and are hypothetical peripheral compartments in the body. One of
the peripheral compartments, for example, may represent well
perfused tissue and the other poorly perfused tissue. In the
formulation given here, the volume of the peripheral compartments
is assumed to be equal to V.sub.1 also. Drug moves between the
central compartment (the plasma) and one of the peripheral
compartments bidirectionally with rate constants k.sub.31 and
k.sub.13. Similarly, drug moves bidirectionally between the other
peripheral compartment and the central compartment with rate
constants k.sub.21 and k.sub.12. The data specifying the values for
these constants that should be used for a particular drug and
patient characteristics are stored in ROM 104 (FIG. 3). Using the
model, the method described above is effected to control the
infusion rate, k.sub.0 (t), of the infusion device to achieve a
value of C.sub.1 (t) that equals the specified plasma drug
concentration.
FIG. 6 is a pictorial abstraction of the following system of linear
differential equations that define the three-compartment model:
The Laplace transform of each of Equations 2, 3, and 4 can be taken
and the resulting simultaneous equations manipulated algebraically
to form an equation (transfer function) 5, shown in FIG. 7, which
relates the central compartment drug concentration, i.e., plasma
drug concentration, to the rate of intravenous drug administration,
i.e., k.sub.0 (t).
In Equation 5, FIG. 7, s is the Laplacian operator and the
constants k.sub.31, k.sub.13, k.sub.12, k.sub.21, k.sub.10, and
V.sub.1 are as illustrated in FIG. 6. The actual values of the rate
constants and central compartment volume used depend upon the
particular drug to which the model is applied and upon the
characteristics of the recipient. From Equation 5, expressions for
the concentration of the drug in each of the three compartments of
the model are developed, as shown for Equations 6, 7, and 8 in
FIGS. 8-10, respectively. Each of these expressions is relatively
complex with respect to the number of terms involved, but is
readily solved by microprocessor 100. The values s.sub.1, s.sub.2,
and s.sub.3 comprise the cubic roots of the denominator of Equation
5. C'.sub.i =1, 2, 3, represent the concentration in each of the
respective compartments at the end of a particular infusion
interval, t-t.sub.0, where t is the current real or simulated time
and t.sub.0 is the real or simulated time at the end of the
previous infusion interval, i.e., at the end of the previous
.DELTA.t. Accordingly, at the end of each successive infusion
interval, C.sub.1 (t), C.sub.2 (t), and C.sub.3 (t) can be computed
in Equations 6, 7, and 8. C.sub.1 (t), C.sub.2 (t), and C.sub.3 (t)
are the state variables in this system of equations and, along with
the aforementioned constants, completely describe the system at any
point in time.
Although the present invention is described with respect to use of
a three-compartment model, it should be apparent that other models
may be used to determine the drug infusion rates necessary to
achieve a specified plasma drug concentration in a pharmacokinetic
model-based infusion device. In a more general sense, it should be
apparent that the present invention is applicable to virtually any
automatic control paradigm in which the relationship between the
output of the controlled actuator and the output of the process to
be controlled is described by a linear dynamic model.
It will further be apparent that modifications may be made to the
present invention within the scope of the claims that follow.
Accordingly, the invention is not in any way intended to be limited
by the disclosure of the preferred embodiments but is defined
entirely by reference to the claims.
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